[Physics] Forces of reaction and torque of water flowing out of a vessel

bernoulli-equationfluid dynamics

Consider the problem wherein we are told to find out the force of reaction of water flowing out of a vessel through an orifice. I attempt to compare it with a shotgun and a bullet as a conservation of momentum of the system. Another approach is Newton's third law that is inextricably related to momentum conservation. However, I can't picture what forces are interacting: how or in what directions. If there were no friction on the floor, would the vessel be pushed in the opposite direction of the water?

There's a second problem about figuring out the reaction moment of water flowing out of a tube, I think the tube's wall interacts with water; what other interactions would there be? Aren't those forces applied in all directions? Do the forces cancel each other or not? Here's a picture of what I think. I learnt a way to calculate the resultant force in this case using linear momentum, but I would like to know the direction of the net force, not only its modulus.

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Here's the problem picture

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Finally, there's a problem about finding out the horizontal force that tends to pull the tube out of the tank. I think the forces interacting should be the same as above with the difference that forces are acting on the tube this time, but it's kind of difficult to picture a resultant force since they appear to cancel each other. Ignoring what I just wrote, since the orifice is small we can assume pressure is the same in all the points of it (that's my idea), so:

$$ dF = ds P $$

I still can not locate the force. Here's the picture of the problem:

enter image description here

Best Answer

Consider the folowing image:


It depects the cross section of a pipe, where one should imagine the water tank on the left. Let's consider a control volume, the dashed lines. Due to the water pressure, the walls exert a force on the water, and so does the water outside the control volume. But let's look at the bottom of our control volume. There are no forces there, since there's nothing underneath it! This means that there is a resultant downwards force on our control volume, and it will flow out as expected

A keen reader will notice that I neglected air pressure. However, since the air pressure works both on the top of our water tank and the bottom of our tap, it will cancel out. This of course only applies to an open water tank.